Question

Dirk Ward borrowed $14,000 for irvestment purposes on May19 on a demand note providing for a variable rate of interest and payment of any accrued interest on December 31. He paid $600 on lune 27, $150 on September 21 , and $1000 on November 16. How much is the accrued interest on December 31 if the rate of interest was 8% on May 19,8.4% effective August 1, and 9% effective November 1 ?

Answer 1

To find the accrued interest for Dirk's loan, one must calculate the interest accrued at each varying interest rate period after accounting for partial payments made. The steps include determining the principal at each rate, calculating interest for each period, and summing the total interest.

Step-by-step explanation:

The student's question involves finding the accrued interest on a demand note with variable rates of interest for a loan that had multiple payments before the year-end. The interest rates changed during the year, affecting the calculation. Here's how to calculate the accrued interest:

1. First, determine the amount of principal subject to interest at each rate.
2. Next, calculate the interest accrued during each period using the appropriate rate.
3. Finally, sum the interest accrued across all periods, taking into account any principal payments made during the year.

Dirk borrowed $14,000 and made three payments throughout the year: $600 on June 27, $150 on September 21, and $1,000 on November 16. The interest rates were 8% from May 19 to July 31, 8.4% from August 1 to October 31, and 9% from November 1 to December 31. To calculate the total accrued interest, we use the formula for simple interest I = P*r*t, where I is the interest, P is the principal, r is the rate, and t is the time in years.